Abstract. We examine massive particles and null geodesics for the scalar-tensor black hole in the Horndeski-Galileon framework. Our analysis shows that first kind relativistic orbits, corresponding to circular and elliptic orbits, are absent for the black hole solution with the static scalar field. This is a highly pathological behavior contradicting to the black hole accretion and Solar System observations.

We examine observational signatures of the asymptotically de Sitter branch of static spherically symmetric Horndeski/Galileon solutions. Our analysis reveales that possible deviations of the photon sphere size from those of the GR Schwarzshild solution are vanishing compared to the resolution of modern radio-interferometric observations. These deviations are heavily suppressed by the bounds coming from the weak-field observation. We conclude that shadow size would not be a useful characteristic to distinguish the Horndeski/Galileon static spherically symmetric spacetimes in the foreseeable future.